In Kentucky, 52 percent of voters said Paul's views were too extreme, but the libertarian-leaning ophthalmologist rode a wave of strong anti-President Obama sentiment in the state. By a 23-point margin, voters there said they were casting their ballots in opposition to Obama, with 62 percent disapproving of Obama's job performance overall, according to ABC News exit polls.
The sentiment was similar in West Virginia, despite a Senate victory for Democratic Gov. Joe Manchin. The state has voted Republican in the last three presidential elections. Seven in 10 disapproved of Obama's job performance, with approval at 30 percent. Nearly half of West Virginia voters said their vote was to express opposition to Obama, while far fewer -- 14 percent -- said they voted to express support for the president.
Exit poll results also underscored the economic distress defining the 2010 election. Eighty-eight percent of voters said the national economy's in bad shape, nearly as many as the record 92 percent who said so two years ago. Only 14 percent said their own family's financial situation has improved since 2008.
"Will the president take a lesson away from tonight?" House Tea Party caucus founder Michele Bachmann asked Tuesday on ABC News Now. "This is a profound repudiation of his policies."
ABC News' Gary Langer contributed to this report.